This isn't quite like idling a normal unicycle, you need more pressure on the top foot on a Coker. But otherwise this is pretty much the same thing.
On a smaller unicycle I'd use a different pedal position, with the back pedal lower. On a Coker you have to spring up onto it, with a smaller wheel it's more like stepping up.
This is apparently not possible on a Coker. I find it the easiest mount to use on road or on mild offroad as you are totally in control at the start and it's easier to go into idling if you need to wait for something in front of you to get out of the way.
This is a very small set of stairs and is the first set I rode on. To ride down stairs, don't do any of that hopping stuff, just pretend that it's a slope at the angle of the stairs and go for it. If you're having trouble going for it, try starting from right near the top so you have to do any thinking before you get on the uni. For bigger stairs, try doing half of the steps to start with, starting with your wheel jammed back on a step. I'll put a bigger better stairs video up soon.
A decent size twelve normal steps followed by five easy steps